34 Transactions of tlic South African Philosophical Society. 



Let 2h be the length of the base and a the angle subtended by it 

 at a distance y. Then — 



7/ = 6 cot " 



du 



da 



y 2sin^" 



A 



da 



sni a 



Let xii^yth of an inch or 0*25 mm. be the admissible error on the- 

 plan, 8 kilometres the limiting value of y, and A« = 20". On the 

 scale of the Canadian photographic surveys, 4tv^o(m the maximum 



error allowable will be 10 metres at 8 kilometres, or ■ — . Then 



y SOU 



o = 4° 27' and 2/>:=620 metres. 



By increasing the base to 2 kilometres a maximum possible- 

 accuracy at 8 kilometers of o-^Vo o^ the distance or 3 metres, would 

 be attained, but the area mapped would be reduced to a narrow 

 strip. 



With the base of 620 metres, the area mapped with a plate of 

 diameter equal to the focal length of the lens would be contained 

 between the limiting circles at 8 and 2*5 kilometres shown at d and 

 n (Fig. 5) and would amount to 22 square kilometres on either side 

 of the base, or, more correctly, to that portion not masked by the 

 nearer topographical features. 



The error in ,r will be due to that in y and that of the ,r co-ordi- 

 nate on the plate. We may write — 



(A^)-^: 



'^/V + f^A, 



/ J • \y 



With a lens of 150 mm. focal lengtli 

 and an error of -025 mm. in the plate-^ 

 a-'s, the maximum error is, for the base 

 and the scale of plan considered, 5 metres, 

 or on the plan 0"12 mm. 



The error in height is given by the 

 same expression. At the maxnnum 

 distance the second term cannot exceed 



the base and the distant points does 

 not exceed 2,000 metres. In absolute 

 amount the total error for points at 

 extreme distances would be + 2-75 metres. 



if the difference in height between 



